Blind Source Signal Separation and Retrieval

近年来，随着高速数字计算机的快速发展，一次处理海量数据已成为可能。在本研究中，我们使用输出信号的二阶和/或四阶累积量来考虑由多个源信号驱动的离散时间线性信道系统的盲解卷积(或盲均衡)。我们提出了几种均衡器的设计方法，并通过数字仿真研究了这些方法的有效性。大体上来说，均衡器的设计有两种方法。(1)第一种方法是从信道输出盲辨识信道系统，然后相应地设计均衡器。(2)第二种方法是直接从均衡器输出设计均衡器。第二种方法称为直接方法，因为它绕过了盲系统辨识过程，也绕过了信道系统的阶次估计。我们致力于采取直接的方法进行研究。我们提出了解决盲反卷积问题的新准则。基于这些准则，提出了盲解卷积的迭代算法，并通过数字仿真研究了所提算法的有效性，为FIR信道系统的盲解卷积奠定了系统理论基础。在此基础上，我们证明了每个可均衡的信道系统都有一个FIR不可约-仿酉分解。基于这一事实，我们证明了任何可均衡的信道系统都可以被称为白化器的滤波器约化为仿酉FIR系统。我们相信，这一系统理论基础为我们进一步设计先进的均衡器提供了原则。

Recently, with the rapid development of high-speed digital computers, it is practically possible to processing a huge size of data all at once. In this research, we considered blind deconvolution ( or blind equalization) of a discrete-time linear channel system driven by multiple source signals using the second-order and/or the fourth-order cumulants of the output signals. We proposed several procedures for designing equalizers and investigated the effectiveness of the proposed procedures through digital simulations.Roughly speaking, there are two approaches to design equalizers.(1) The first approach is to blindly identify the channel system from the channel outputs and then to design an equalizer accordingly.(2) The second approach is directly to design an equalizer from the equalizer outputs.The second approach is called the direct approach, which is preferable, because it bypasses the process of blind system identification, and also bypasses the order estimation of the channel system. We devoted ourselves to take the direct approach in this research.We proposed new criteria for solving the blind deconvolution problem. Base on these criteria, we developed iterative algorithms for attaining blind deconvolution, and then we investigated the effectiveness of the proposed algorithms through digital simulations.Moreover, we established a system-theoretical foundation for the blind deconvolution of an FIR channel system. In this fundamental setting, we showed that every equalizable channel system has an FIR irredusible-paraunitary factorization. Based on this fact, we showed that any equalizable channel system can be reduced to a paraunitary FIR systemby a filter called a whitener. We believe that the system-theoretical foundation gives us a principle for designing futther advanced equalizers.